Question

a bullet is moving with a velocity of 100 m/s can just penetrate two planks of equal thickness. the number of such planks penetrated by the same bullet when the velocity is doubled will be :- (1) 4 (2) 6 (3) 8 (4) 10

Answer 1

Assume uniform retardation of the bullet inside the plank.

Use the formula $v^2=u^2-2as$, where $a$ is the deceleration, $s$, the distance penetrated.

We have,

$0=u^2-2as ,s=\frac{u^2}{2a}$. Now, when the velocity is doubled,

$s'=\frac{4u^2}{2a}=4s$.

When the velocity is doubled, the distance penetrated is 4 times the original distance. So the number of planks will be 4 times 2 planks.

That is $8$ planks.

The correct choice is (3).